Objective Bayesian Comparison of Order-Constrained Models in Contingency Tables.

In social and biomedical sciences, testing in contingency tables often involves order restrictions on cell
probabilities parameters. We develop objective Bayes methods for order-constrained testing and model
comparison when observations arise under product binomial or multinomial sampling. Specifically, we
consider tests for monotone order of the parameters against equality of all parameters. Our strategy
combines in a unified way both the intrinsic prior methodology and the encompassing prior approach in
order to compute Bayes factors and posterior model probabilities. Performance of our method is evaluated
on several simulation studies and real datasets.